Use our free GCF of Fractions Calculator tool to compute the GCF of 340/917, 322/289 i.e 2/265013 easily. The following is the detailed procedure to determine the greatest common factor of fractions 340/917, 322/289.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 340/917,322/289
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 340/917,322/289, numerators are 340,322
Denominators are 917,289
The GCF of 340,322 is 2 .
LCM of 917,289 is 265013.
The greatest common factor of 340/917,322/289 = [GCF of 340,322]/[LCM of 917,289]= 2/265013
Therefore, the GCF of 340/917,322/289 is 2/265013.
To find the highest common factor of 340,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 340,322 is 2.
Lets's calculate GCF of 340,322
2 | 340, 322 |
170, 161 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 340
:1,2,4,5,10,17,20,34,68,85,170,340
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 340,322 . The biggest common factor number is the GCF number.
So the greatest common factor 340,322 is 2.
Lets's calculate LCM of 917,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 265013
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/265013
Therefore, the GCF of Fractions 340/917,322/289 is 2/265013
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 917,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(917,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(917,289) x common factors =1 x 1 = 1
LCM(917,289) = ( 917 × 289 ) / 1
LCM(917,289) = 265013 / 1
LCM(917,289) = 265013
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 340,322?
The HCF of 340,322 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 340/917, 322/289?
Answer: GCF of Numerators as per given numbers 340/917, 322/289 is
GCF of Numerators i.e. for 340,322 is 2
LCM of denominators i.e. for 917,289 is 265013.
Thus, GCF of Fractions is 2/265013.Finally, GCF of Fractions for 340/917, 322/289 is 2/265013.